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4-2.Quadratic Equations and Inequations
hard
यदि $a + b + c =1, ab + bc + ca =2$ तथा $abc =3$ हैं, तो $a ^{4}+ b ^{4}+ c ^{4}$ बराबर है ................ |
A
$13$
B
$15$
C
$17$
D
$21$
(JEE MAIN-2021)
Solution
${a^{2}+b^{2}+c^{2}=(a+b+c)^{2}-2 \Sigma a b=-3}$
${(a b+b c+c a)^{2}=\Sigma(a b)^{2}+2 a b c \sum a}$
${\Rightarrow \Sigma(a b)^{2}=-2}$
${a^{4}+b^{4}+c^{4}=\left(a^{2}+b^{2}+c^{2}\right)^{2}-2 \Sigma(a b)^{2}}$
${\quad=9-2(-2)=13}$
Standard 11
Mathematics
